Strange DNS behaviour over VPN

Question

We have a small branch with few computers with few computers connected via the Internet to our central building. We don't use site-to-site, but dial-in to the Cisco router (we use ShrewSoft as a client and pull network configuration from the RADIUS server).

Everything was working just fine, but our tel-co was messing around with something (not clear what) as they had promised. Yesterday I got a call from the branch and they said they could browse the Internet, but can't access our internal web servers. I started investigating and it turned out the VPN settings were all messed up, OK fixed that.

The most interesting part is the DNS stuff. After I restored the VPN, I connected using RDP to their computer and tried pinging our Internal DNS server (192.168.1.31) and Google's DNS (8.8.8.8). That worked fine. I then tried nslookup www.google.com 8.8.8.8 - works fine. Then nslookup www.google.com 192.168.1.31 - that works fine! BUT trying to resolve any of our internal addresses fails. We have a few of DNS servers and all of them fail. Looks like the reply never gets back. From internal network it works fine. But how does that happen: nslookup resolves our dns server's FQDN using reverse lookup?? It doesn't have anything to do with firewalls, right? Reverse lookup gets a reply. Help me please, in which direction should I look?

PS. To the left of the cloud is our central building, to the right - branch.

PPS. I've written the needed records to the hosts file just as a temporary workaround so they could do their job.

PPPS. Cannot really check with other computers in branch as they don't use VPN and the employees there are in their 60s so they don't understand a thing and can do only very simple things.